Chen & Hatschka prove core stability for multi-winner voting under TU/NTU models

A new paper on arXiv (2605.22528) by Jiehua Chen and Christian Hatschka tackles a fundamental question in multi-winner approval voting: when can a committee resist coalition defections? The concept of core-stable committees, introduced by Aziz et al. (2017), ensures no coalition can propose a smaller committee that gives all its members strictly more approved alternatives. The authors generalize this into 'multi-winner voting games'—a cooperative-game framework that models voters as players with proportional seat caps. They consider two utility-transfer models: transferable utility (TU), where coalitions can redistribute total utility from an admissible committee, and non-transferable utility (NTU), where utility vectors must come directly from a committee.

The paper systematically studies core existence and computation under four prominent voting rules: Approval Voting (AV), Satisfaction Approval Voting (SAV), Chamberlin-Courant (CC), and Proportional Approval Voting (PAV). The NTU-core recovers the classic core-stable committee notion, while the TU-core is introduced for the first time in this context. By analyzing when the core is always non-empty, the authors provide a unified lens for understanding coalitional stability across different voting rules and utility assumptions. This work bridges cooperative game theory and computational social choice, with implications for designing stable committee selection mechanisms in decentralized governance and participatory budgeting.